Acoustophoretic separation technology using multi-dimensional standing waves

ABSTRACT

A system having improved trapping force for acoustophoresis is described where the trapping force is improved by manipulation of the frequency of the ultrasonic transducer. The transducer includes a ceramic crystal. The crystal may be directly exposed to fluid flow. The crystal may be air backed, resulting in a higher Q factor.

This application is a continuation-in-part of U.S. application Ser. No.15/647,223, filed Jul. 11, 2017, which is a continuation of U.S. Ser.No. 15/285,434, filed Oct. 4, 2016, now U.S. Pat. No. 9,701,955, whichis a continuation of U.S. Ser. No. 14/026,413, filed Sep. 13, 2013, nowU.S. Pat. No. 9,485,450, which is a continuation-in-part of U.S. Ser.No. 13/844,754, filed Mar. 15, 2013, which claims the benefit of U.S.Provisional Patent Application Ser. No. 61/611,159, filed Mar. 15, 2012,and which claims the benefit of U.S. Provisional Patent Application Ser.No. 61/611,240, filed Mar. 15, 2012, and which claims the benefit ofU.S. Provisional Patent Application Ser. No. 61/708,641, filed on Oct.2, 2012, and which claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/754,792, filed Jan. 21, 2013. This applicationclaims the benefit of U.S. Provisional Patent Application Ser. No.62/412,759, filed Oct. 25, 2017. The entire disclosures of all of theabove-referenced applications are hereby incorporated herein byreference.

BACKGROUND

Acoustophoresis is the separation of particles using high intensitysound waves. It has long been known that high intensity standing wavesof sound can exert forces on particles. A standing wave has a pressureprofile which appears to “stand” still in time. The pressure profile ina standing wave varies from areas of high pressure (nodes) to areas oflow pressure (anti-nodes). Standing waves are produced in acousticresonators. Common examples of acoustic resonators include many musicalwind instruments such as organ pipes, flutes, clarinets, and horns.

BRIEF DESCRIPTION

The present disclosure relates to systems and devices foracoustophoresis on preferably a large scale. The devices use one or moreunique ultrasonic transducers as described herein, or an array of suchtransducers. The transducer is driven at frequencies that producemulti-dimensional standing waves.

In some embodiments, an apparatus is disclosed that includes a flowchamber with at least one inlet and at least one outlet through which amixture of a host fluid and at least one of a second fluid and aparticulate is flowed. At least one ultrasonic transducer is embedded ina wall of said flow chamber or located outside the flow chamber wall andis driven by an oscillating, periodic, modulated, or pulsed voltagesignal of ultrasonic frequencies which drives the transducer in a higherorder mode of vibration to create multi-dimensional standing waves inthe flow channel. The transducer includes a ceramic crystal or otherpiezoelectric material having certain vibration characteristics. A solidor flexible reflector is located on the wall on the opposite side of theflow chamber from the transducer. The apparatus may further include anapparatus inlet that feeds into an annular plenum, as well as twooutlets located on different walls of the apparatus.

In other embodiments, a method of separating a host fluid from at leastone of a second fluid and/or a particulate is disclosed. The methodcomprises flowing the host fluid into a flow chamber having a resonatorand a collection pocket or port and driving a transducer with anoscillating, periodic, modulated, or pulsed voltage signal to createstanding waves of a multi-dimensional nature with the resonator andcollect the at least one of the second fluid and/or particulate in thecollection pocket.

In yet other embodiments, an apparatus comprises a flow chamber with atleast one inlet and at least one outlet through which a mixture of ahost fluid and at least one of a second fluid and a particulate isflowed. A plurality of ultrasonic transducers are embedded in a wall ofsaid flow chamber or located outside the flow chamber wall. Thetransducers each include a ceramic crystal or other piezoelectricmaterial driven by an oscillating, periodic, modulated, or pulsedvoltage signal of ultrasonic frequencies which drives the transducers ina higher order mode of vibration to create multi-dimensional standingwaves in the flow channel. A solid or flexible reflector is located onthe wall on the opposite side of the flow chamber from the transducers.The apparatus may further include an apparatus inlet that feeds into anannular plenum, as well as two outlets located on different walls of theapparatus.

These and other non-limiting characteristics are more particularlydescribed below.

BRIEF DESCRIPTION OF THE DRAWINGS

The following is a brief description of the drawings, which arepresented for the purposes of illustrating the exemplary embodimentsdisclosed herein and not for the purposes of limiting the same.

FIG. 1A is a diagram illustrating the function of an acoustophoreticseparator with a second fluid or particle less dense than the hostfluid.

FIG. 1B is a diagram illustrating the function of an acoustophoreticseparator with a second fluid or particle denser than the host fluid.

FIG. 2A shows a cell size distribution produced by a Jorin ViPA ParticleSize Analyzer when there was no acoustic field present. The horizontalaxis is the size class, in microns, and the vertical axis is the percentof particles sampled by volume.

FIG. 2B shows a cell size distribution produced by a Jorin ViPA ParticleSize Analyzer when there was an acoustic field present. The horizontalaxis is the size class, in microns, and the vertical axis is the percentof particles sampled by volume.

FIG. 3 shows an acoustophoretic separator having a plurality oftransducers.

FIG. 4A is a detail view of a diffuser used as an inlet in the separatorof FIG. 3.

FIG. 4B is a detail view of an alternate inlet diffuser that can be usedwith the separator of FIG. 3.

FIG. 5 is a cross-sectional diagram of a conventional ultrasonictransducer.

FIG. 6 is a picture of a wear plate of a conventional transducer.

FIG. 7A is a cross-sectional diagram of an ultrasonic transducer of thepresent disclosure. An air gap is present within the transducer, and nobacking layer or wear plate is present.

FIG. 7B is a cross-sectional diagram of an ultrasonic transducer of thepresent disclosure. An air gap is present within the transducer, and abacking layer and wear plate are present.

FIG. 8 is a computer model of an acoustophoretic separator simulated togenerate FIG. 9 and FIGS. 11-17.

FIGS. 9A-9D show simulations of the forces on a particle in anacoustophoretic separator. FIG. 9A shows the axial force for a singlestanding wave. The text at the top of the scale on the right is“×10⁻¹¹”. FIG. 9B shows the lateral force for a single standing wave.The text at the top of the scale on the right is “×10⁻¹³”. FIG. 9C showsthe axial force with a multi-mode excitation. The text at the top of thescale on the right is “×10⁻¹⁰”. FIG. 9D shows the lateral force with amulti-mode excitation. The text at the top of the scale on the right is“×10⁻¹¹”. For all figures, the horizontal axis is the location along theX-axis of FIG. 8 within the chamber, in inches, and the vertical axis isthe location along the Y-axis of FIG. 8 within the chamber, in inches.The scale on the right of each figure is in Newtons.

FIG. 10 is a picture of a simulated crystal showing the mode shapedisplacement in a crystal. The text for the x-axis reads ×10⁻³”. Thetext for the z-axis includes “×10⁻³” and “×10⁻⁴”.

FIGS. 11-17 are additional simulations of the forces on a particle in anacoustophoretic separator. The horizontal axis is the location along theX-axis of FIG. 8 within the chamber, in inches, and the vertical axis isthe location along the Y-axis of FIG. 8 within the chamber, in inches.The scale on the right is in Newtons (N) for all figures except FIG. 13.In FIG. 13, the scale on the right is in Pascals (Pa).

The text at the top of the scale on the right in FIG. 11 is “×10⁻¹⁰”.

The text at the top of the scale on the right in FIG. 12 is “×10⁻¹⁰”.

The text at the top of the scale on the right in FIG. 13 is “×10⁶”. Thetext at the top by the upward-pointing triangle reads “2.5166×10⁶”. Thetext at the bottom by the downward-pointing triangle reads “507.16”.These two triangles show the maximum and minimum values depicted in thisfigure.

The text at the top of the scale on the right in FIG. 14 is “×10⁻¹²”.The text at the top by the upward-pointing triangle reads“4.3171×10⁻¹⁰”. The text at the bottom by the downward-pointing trianglereads “−4.3171×10⁻¹⁰”. These two triangles show the maximum and minimumvalues depicted in this figure.

The text at the top of the scale on the right in FIG. 15 is “×10⁻¹¹”.The text at the top by the upward-pointing triangle reads “2.0156×10⁻⁹”.The text at the bottom by the downward-pointing triangle reads“−2.0058×10⁻⁹”. These two triangles show the maximum and minimum valuesdepicted in this figure.

The text at the top of the scale on the right in FIG. 16 is “×10⁻¹²”.The text at the top by the upward-pointing triangle reads“1.4606×10⁻¹⁰”. The text at the bottom by the downward-pointing trianglereads “−1.4604×10⁻¹⁰”. These two triangles show the maximum and minimumvalues depicted in this figure.

The text at the top of the scale on the right in FIG. 17 is “×10⁻¹¹”.The text at the top by the upward-pointing triangle reads“4.0239×10⁻¹⁰”. The text at the bottom by the downward-pointing trianglereads “−4.4353×10⁻¹⁰”. These two triangles show the maximum and minimumvalues depicted in this figure.

FIG. 18 is a graph showing the relationship of the acoustic radiationforce, buoyancy force, and Stokes' drag force to particle size. Thehorizontal axis is in microns (μm) and the vertical axis is in Newtons(N).

FIG. 19 is a photo of a square transducer and a circular transducer foruse in an acoustophoretic separator.

FIG. 20 is a graph of electrical impedance amplitude versus frequencyfor a square transducer driven at different frequencies.

FIG. 21A illustrates the trapping line configurations for seven of thepeak amplitudes of FIG. 20 from the direction orthogonal to fluid flow.

FIG. 21B is a perspective view illustrating the separator. The fluidflow direction and the trapping lines are shown.

FIG. 21C is a view from the fluid inlet along the fluid flow direction(arrow 114) of FIG. 21B, showing the trapping nodes of the standing wavewhere particles would be captured.

FIG. 21D is a view taken through the transducers face at the trappingline configurations, along arrow 116 as shown in FIG. 21B.

FIG. 22 is a photo of the nine-trapping-line configuration of a standingwave created by the multi-modal displacement of the transducer for anoil-water emulsion.

FIG. 23 is a zoom-in photo of FIG. 22 showing the upper three trappinglines of the nine-trapping-line configuration.

FIG. 24 is a computer simulation of the acoustic pressure amplitude(right-hand scale in Pa) and transducer out of plane displacement(left-hand scale in meters). The text at the top of the left-hand scalereads “×10⁻⁷”. The text at the top of the left-hand scale by theupward-pointing triangle reads “1.473×10⁻⁶”. The text at the bottom ofthe left-hand scale by the downward-pointing triangle reads“1.4612×10⁻¹⁰”. The text at the top of the right-hand scale reads“×10⁶”. The text at the top of the right-hand scale by theupward-pointing triangle reads “1.1129×10⁶”. The text at the bottom ofthe right-hand scale by the downward-pointing triangle reads “7.357”.The triangles show the maximum and minimum values depicted in thisfigure for the given scale. The horizontal axis is the location withinthe chamber along the X-axis in FIG. 8, in inches, and the vertical axisis the location within the chamber along the Y-axis in FIG. 8, ininches.

FIG. 25 and FIG. 26 show transducer array configurations.

FIG. 27A shows an acoustophoretic separator for separating buoyantmaterials for use with the transducers of FIGS. 23 and 24.

FIG. 27B is a magnified view of fluid flow near the intersection of thecontoured nozzle wall 129 and the collection duct 137.

FIG. 28 is a computer simulation of the acoustic pressure amplitude ofthe ultrasonic waves generated by an array of transducers.

FIG. 29 is a photo showing the trapping lines for oil droplets in theultrasonic waves generated by an array of transducers.

FIG. 30 is a photo showing the trapping lines for oil droplets in theultrasonic waves generated by an array of transducers.

FIG. 31 is a computer simulation of acoustic pressure amplitude.

FIG. 32 shows a depiction of symmetric Lamb waves and anti-symmetricLamb waves.

FIG. 33 shows the In-Plane and Out-of-Plane displacement of a crystalwhere composite waves are present.

FIGS. 34A, 34B, 34C and 34D illustrate the (1,1) vibration mode of arectangular plate. FIG. 34A is a perspective view. FIG. 34B is the viewalong the length of the plate. FIG. 34C is the view along the width ofthe plate. FIG. 34D shows the in-plane displacement of the rectangularplate vibrating at the (1,1) mode.

FIGS. 35A, 35B and 35C illustrate the (1,2) vibration mode of arectangular plate. FIG. 35A is a perspective view. FIG. 35B is the viewalong the length of the plate. FIG. 35C is the view along the width ofthe plate.

FIGS. 36A, 36B and 36C illustrate the (2,1) vibration mode of arectangular plate. FIG. 36A is a perspective view. FIG. 36B is the viewalong the length of the plate. FIG. 36C is the view along the width ofthe plate.

FIGS. 37A, 37B and 37C illustrate the (2,2) vibration mode of arectangular plate. FIG. 37A is a perspective view. FIG. 37B is the viewalong the length of the plate. FIG. 37C is the view along the width ofthe plate.

FIGS. 38A, 38B, 38C and 38D illustrate the (3,3) vibration mode of arectangular plate. FIG. 38A is a perspective view. FIG. 38B is the viewalong the width of the plate. FIG. 38C is the view along the length ofthe plate. FIG. 38D shows the in-plane displacement of the rectangularplate vibrating at the (3,3) mode.

FIG. 39A shows the pressure field created in water at a (1,1) vibrationmode.

FIG. 39B shows the pressure field created in water at a (2,2) vibrationmode. FIG. 39C shows the pressure field created in water at a (3,3)vibration mode.

FIG. 40A shows an exploded view of an acoustophoretic separator used inBio-Pharma applications.

FIG. 40B shows an exploded view of a stacked acoustophoretic separatorwith two acoustic chambers.

FIG. 41A is a graph showing the efficiency of removing cells from amedium using a Beckman Coulter Cell Viability Analyzer for oneexperiment.

FIG. 41B is a graph showing the efficiency of removing cells from amedium using a Beckman Coulter Cell Viability Analyzer for anotherexperiment.

DETAILED DESCRIPTION

The present disclosure may be understood more readily by reference tothe following detailed description of desired embodiments and theexamples included therein. In the following specification and the claimswhich follow, reference will be made to a number of terms which shall bedefined to have the following meanings.

The singular forms “a,” “an,” and “the” include plural referents unlessthe context clearly dictates otherwise.

As used in the specification and in the claims, the term “comprising”may include the embodiments “consisting of” and “consisting essentiallyof.”

Numerical values should be understood to include numerical values whichare the same when reduced to the same number of significant figures andnumerical values which differ from the stated value by less than theexperimental error of conventional measurement technique of the typedescribed in the present application to determine the value.

All ranges disclosed herein are inclusive of the recited endpoint andindependently combinable (for example, the range of “from 2 grams to 10grams” is inclusive of the endpoints, 2 grams and 10 grams, and all theintermediate values).

As used herein, approximating language may be applied to modify anyquantitative representation that may vary without resulting in a changein the basic function to which it is related. Accordingly, a valuemodified by a term or terms, such as “about” and “substantially,” maynot be limited to the precise value specified. The modifier “about”should also be considered as disclosing the range defined by theabsolute values of the two endpoints. For example, the expression “fromabout 2 to about 4” also discloses the range “from 2 to 4.”

It should be noted that many of the terms used herein are relativeterms. For example, the terms “upper” and “lower” are relative to eachother in location, i.e. an upper component is located at a higherelevation than a lower component in a given orientation, but these termscan change if the device is flipped. The terms “inlet” and “outlet” arerelative to a fluid flowing through them with respect to a givenstructure, e.g. a fluid flows through the inlet into the structure andflows through the outlet out of the structure. The terms “upstream” and“downstream” are relative to the direction in which a fluid flowsthrough various components, i.e. the flow fluids through an upstreamcomponent prior to flowing through the downstream component. It shouldbe noted that in a loop, a first component can be described as beingboth upstream of and downstream of a second component.

The terms “horizontal” and “vertical” are used to indicate directionrelative to an absolute reference, i.e. ground level. However, theseterms should not be construed to require structures to be absolutelyparallel or absolutely perpendicular to each other. For example, a firstvertical structure and a second vertical structure are not necessarilyparallel to each other. The terms “top” and “bottom” or “base” are usedto refer to surfaces where the top is always higher than the bottom/baserelative to an absolute reference, i.e. the surface of the earth. Theterms “above” and “below”, or “upwards” and “downwards” are alsorelative to an absolute reference; an upwards flow is always against thegravity of the earth.

The present application refers to “the same order of magnitude.” Twonumbers are of the same order of magnitude if the quotient of the largernumber divided by the smaller number is a value less than 10.

Discussed herein are efficient separation technologies formulti-component liquid streams that reduce or eliminate waste and reducethe energy used, and therefore promote a sustainable environment. Largevolume flow rate acoustophoretic phase separator technology usingultrasonic standing waves provides the benefit of having no consumables,no generated waste, and a low cost of energy. The technology isefficient at removal of particles of greatly varying sizes, includingseparation of micron and sub-micron sized particles. Examples ofacoustic filters/collectors utilizing acoustophoresis can be found incommonly owned U.S. patent application Ser. Nos. 12/947,757; 13/085,299;13/216,049; and Ser. No. 13/216,035, the entire contents of each beinghereby fully incorporated by reference.

The platform technology described herein provides an innovative solutionthat includes a large volume flow rate acoustophoretic phase separatorbased on ultrasonic standing waves with the benefit of having noconsumables, no generated waste, and a low cost of energy.Acoustophoresis is a low-power, no-pressure-drop, no-clog, solid-stateapproach to particle removal from fluid dispersions: i.e., it is used toachieve separations that are more typically performed with porousfilters, but it has none of the disadvantages of filters. In particular,the present disclosure provides systems that operate at the macro-scalefor separations in flowing systems with high flow rates. The acousticresonator is designed to create a high intensity three dimensionalultrasonic standing wave that results in an acoustic radiation forcethat is larger than the combined effects of fluid drag and buoyancy orgravity, and is therefore able to trap (i.e., hold stationary) thesuspended phase to allow more time for the acoustic wave to increaseparticle concentration, agglomeration and/or coalescence. The presentsystems have the ability to create ultrasonic standing wave fields thatcan trap particles in flow fields with a linear velocity ranging from0.1 mm/sec to velocities exceeding 1 cm/s. This technology offers agreen and sustainable alternative for separation of secondary phaseswith a significant reduction in cost of energy. Excellent particleseparation efficiencies have been demonstrated for particle sizes assmall as one micron.

The acoustophoretic separation technology employs ultrasonic standingwaves to trap, i.e., hold stationary, secondary phase particles in ahost fluid stream. The trapping of particles is an important distinctionfrom previous approaches where particle trajectories were merely alteredby the effect of the acoustic radiation force. The scattering of theacoustic field off the particles results in a secondarythree-dimensional acoustic radiation force. The pressure profilegenerated by the three-dimensional acoustic standing wave acts as athree-dimensional trapping field. The acoustic radiation force isproportional to the particle volume (e.g. the cube of the radius) whenthe particle is small relative to the wavelength. It is proportional tofrequency and the acoustic contrast factor. It also scales with acousticenergy (e.g. the square of the acoustic pressure amplitude). Forharmonic excitation, the sinusoidal spatial variation of the force iswhat drives the particles to the stable positions within the standingwaves. When the acoustic radiation force exerted on the particles isstronger than the combined effect of fluid drag force andbuoyancy/gravitational force, the particle is trapped within theacoustic standing wave field. The action of the acoustic forces on thetrapped particles results in concentration, agglomeration and/orcoalescence of particles and droplets. Additionally, secondaryinter-particle forces, such as Bjerkness forces, aid in particleagglomeration. Heavier-than-the-host-fluid (i.e. denser than the hostfluid) particles and/or fluids are separated through enhancedgravitational settling, and lighter-than-the-host-fluid particles and/orfluids are separated through enhanced buoyancy.

It is also possible to drive multiple ultrasonic transducers witharbitrary phasing. In other words, the multiple transducers may work toseparate materials in a fluid stream while being out of phase with eachother. Alternatively, a single ultrasonic transducer that has beendivided into an ordered array may also be operated such that somecomponents of the array will be out of phase with other components ofthe array.

Efficient and economic particle separation processes can be useful inmany areas of energy generation, e.g., producing water, hydro-fracking,and bio-fuels, e.g, harvesting and dewatering. Acoustophoretictechnology can be used to target accelerated capture of bacterial sporesin water, oil-recovery, and dewatering of bio-oil derived frommicro-algae. Current technology used in the oil recovery field does notperform well in recovery of small, i.e., less than 20 micron, oildroplets. However, the acoustophoretic systems described herein canenhance the capture and coalescence of small oil droplets, therebyshifting the particle size distribution resulting in an overallincreased oil capture. In practice, it is useful to demonstrate largeflow rates at a level of 15-20 gallons per minute (GPM) per square foot(cross-sectional area). Another goal is the increased capture of oildroplets with a diameter of less than 20 microns.

Acoustophoretic separation can also be used to aid such applications asadvanced bio-refining technology to convert low-cost readily availablenon-food biomass (e.g. municipal solid waste and sewage sludge) into awide array of chemicals and secondary alcohols that can then be furtherrefined into renewable gasoline, jet fuel, or diesel. A water treatmenttechnology is used to de-water the fermentation broth and isolatevaluable organic salts for further processing into fuels. The dewateringprocess is currently done through an expensive and inefficientultra-filtration method that suffers from frequent fouling of themembranes, a relatively low concentration factor, and a high capital andoperating expense. Acoustophoretic separation can filter out particleswith an incoming particle size distribution that spans more than threeorders of magnitude, namely from 600 microns to 0.3 microns, allowingimprovements in the concentration of the separated broth with a lowercapital and operational expense. Some other applications are in theareas of wastewater treatment, grey water recycling, and waterproduction.

Acoustophoretic separation is also useful for the harvesting,oil-recovery, and dewatering of micro-algae for conversion into bio-oil.Current harvesting, oil recovery, and dewatering technologies formicro-algae suffer from high operational and capital expenses. Currentbest estimates put the price of a barrel of bio-oil derived frommicro-algae at a minimum of $200.00 per barrel. Acoustophoreticseparation technology can improve harvesting, oil-recovery, anddewatering of micro-algae biofuel.

Other applications are in the area of life sciences and medicalapplications, such as the separation of lipids from red blood cells.Such separation can be of critical importance during cardiopulmonarybypass surgery, which involves suctioning shed mediastinal blood. Lipidsare unintentionally introduced to the bloodstream when blood isre-transfused to the body. Lipid micro-emboli can travel to the brainand cause various neuro-cognitive disorders. Existing methods forremoving lipids are currently inefficient or harmful to red blood cells.

One specific application for the acoustophoresis device is in theprocessing of bioreactor materials. In a fed batch bioreactor, it isimportant at the end of the production cycle to filter all of the cellsand cell debris from the expressed materials that are in the fluidstream. The expressed materials are composed of biomolecules such asrecombinant proteins or monoclonal antibodies, and are the desiredproduct to be recovered. Through the use of acoustophoresis, theseparation of the cells and cell debris is very efficient and leads tovery little loss of the expressed materials. This is an improvement overthe current filtration processes (depth filtration, tangential flowfiltration, centrifugation), which show limited efficiencies at highcell densities, so that the loss of the expressed materials in thefilter beds themselves can be up to 5% of the materials produced by thebioreactor. The use of mammalian cell culture include Chinese hamsterovary (CHO), NS0 hybridoma cells, baby hamster kidney (BHK) cells, andhuman cells has proven to be a very efficacious way ofproducing/expressing the recombinant proteins and monoclonal antibodiesused in pharmaceuticals. The filtration of the mammalian cells and themammalian cell debris through acoustophoresis aids in greatly increasingthe yield of the fed batch bioreactor.

Another type of bioreactor, a perfusion reactor, uses continuousexpression of the target protein or monoclonal antibodies from the CHOcells. The design of such a bioreactor system enables a much smallerfootprint in faster production cycle. The use of acoustophoresis to holdthe CHO cells in a fluid stream as they are producing/expressing theproteins is a very efficient and closed loop way of production. It alsoallows for a maximum production efficiency of the proteins andmonoclonal antibodies in that none of the materials are lost in a filterbed.

In the fed batch bioreactor process, the acoustophoresis device usessingular or multiple standing waves to trap the cells and cell debris.The cells and cell debris, having a positive contrast factor, move tothe nodes (as opposed to the anti-nodes) of the standing wave. As thecells and cell debris agglomerate at the nodes of the standing wave,there is also a physical scrubbing of the fluid stream that occurswhereby more cells are trapped as they come in contact with the cellsthat are already held within the standing wave. When the cells in thestanding wave agglomerate to the extent where the mass is no longer ableto be held by the acoustic wave, the aggregated cells and cell debristhat have been trapped fall out of the fluid stream through gravity, andcan be collected separately. To aid this gravitational settling of thecells and cell debris, the standing wave may be interrupted to allow allof the cells to fall out of the fluid stream that is being filtered fromthe fed batch bioreactor.

Particular embodiments also focus on the capture and growth ofsub-20-micron oil droplets. At least 80% of the volume of sub-20-microndroplets are captured and then grown to droplets that are bigger than 20microns. The process involves the trapping of the oil droplets in theacoustic standing wave, coalescence of many small trapped droplets, andeventually release of the larger droplets when the acoustic trappingforce becomes smaller than the buoyancy force. This design is shown inFIG. 3 where separation of contaminants is not required.

Advanced multi-physics and multiple length scale computer models andhigh frequency (MHz), high-power, and high-efficiency ultrasonic driverswith embedded controls have been combined to arrive at new designs ofacoustic resonators driven by arrays of piezoelectric transducers,resulting in acoustophoretic separation devices that far surpass currentcapabilities.

Desirably, such transducers generate a three-dimensional standing wavein the fluid that exerts a lateral force on the suspendedparticles/secondary fluid to accompany the axial force so as to increasethe particle trapping capabilities of a acoustophoretic system. Typicalresults published in literature state that the lateral force is twoorders of magnitude smaller than the axial force. In contrast, thetechnology disclosed in this application provides for a lateral force tobe of the same order of magnitude as the axial force.

As defined herein, impurities include particles or fluids distinct fromthe host fluid. The acoustic resonator 10 is designed to maintain a highintensity three-dimensional acoustic standing wave. The system is drivenby a function generator and amplifier (not shown). The systemperformance is monitored and controlled by a computer.

The frequency or voltage amplitude of the standing wave can becontrolled or modulated to manage acoustic streaming. The control may beachieved by amplitude modulation and/or by frequency modulation. Theduty cycle of the propagation of the standing wave may also be utilizedto achieve certain results for trapping of materials. In other words,the acoustic beam may be turned on and shut off at different frequenciesto achieve desired results.

A diagrammatic representation of an embodiment for removing oil or otherlighter-than-water material is shown in FIG. 1A. Excitation frequenciestypically in the range from hundreds of kHz to 10s of MHz are applied bytransducer 10. One or more standing waves are created between thetransducer 10 and the reflector 11.

Microdroplets 12 are trapped in standing waves at the pressureanti-nodes 14 where they agglomerate, aggregate, clump, or coalesce,and, in the case of buoyant material, float to the surface and aredischarged via an effluent outlet 16 located above the flow path.Clarified water is discharged at outlet 18. The acoustophoreticseparation technology can accomplish multi-component particle separationwithout any fouling at a much reduced cost.

A diagrammatic representation of an embodiment for removing contaminantsor other heavier-than-water material is shown in FIG. 1B. Excitationfrequencies typically in the range from hundreds of kHz to 10s of MHzare applied by transducer 10. Contaminants in the incoming water 13 aretrapped in standing waves at the pressure nodes 15 where theyagglomerate, aggregate, clump, or coalesce, and, in the case of heaviermaterial, sink to the bottom collector and are discharged via aneffluent outlet 17 located below the flow path. Clarified water isdischarged at outlet 18.

FIG. 2A shows a particle size distribution that was measured as anoil-water emulsion passed through an acoustophoretic system without anacoustic field activated. The peak particle size 20 is between 20-50microns in size without the acoustic field being activated. Thesedroplets are typically very difficult to separate by conventional means,such as, e.g., hydrocyclones.

FIG. 2B shows a similar particle size distribution that was measuredafter an oil-water emulsion passed through an acoustophoretic systemwith the acoustic field activated. The peak particle size 22 is greaterthan 200 microns in size with the acoustic field being activated. Theresults clearly show a significant amount of oil droplet growth, i.e.,many sub-20 micron droplets coalesced, agglomerated, or clumped intolarger droplets (bigger than 20 micron) as a result of the action of theacoustic forces on the droplets.

FIG. 3 shows another embodiment of an acoustophoretic particle separator30. The acoustophoretic separator 30 has an inlet 32 and an outlet 34.The inlet 32 is fitted with a nozzle or diffuser 90 having a honeycomb95 to facilitate the development of plug flow. The acoustophoreticseparator 30 has an array 38 of transducers 40, in this case sixtransducers all arranged on the same wall. The transducers are arrangedso that they cover the entire cross-section of the flow path. Theacoustophoretic separation system of FIG. 3 has, in certain embodiments,a square cross section of 6 inches×6 inches which operates at flow ratesof up to 3 gallons per minute (GPM), or a linear velocity of 8 mm/sec.The transducers 40 are six PZT-8 (Lead Zirconate Titanate) transducerswith a 1 inch diameter and a nominal 2 MHz resonance frequency. Eachtransducer consumes about 28 W of power for droplet trapping at a flowrate of 3 GPM. This translates in an energy cost of 0.25 kW hr/m³, whichprovides an indication of the very low cost of energy of thistechnology. Desirably, each transducer is powered and controlled by itsown amplifier. The application for this embodiment is to shift theparticle size distribution through agglomeration, aggregation, clumpingor coalescing of the micron-sized oil droplets into much largerdroplets, as evident in FIG. 2A and FIG. 2B.

FIG. 4A and FIG. 4B show two different diffusers that can be used at theinlet of the acoustophoretic separator. The diffuser 90 has an entrance92 (here with a circular shape) and an exit 94 (here with a squareshape). The diffuser of FIG. 4A is illustrated in FIG. 3. FIG. 4Aincludes a grid or honeycomb 95, whereas FIG. 4B does not. The gridhelps ensure uniform flow.

FIG. 5 is a cross-sectional diagram of a conventional ultrasonictransducer. This transducer has a wear plate 50 at a bottom end, epoxylayer 52, ceramic crystal 54 (made of, e.g. PZT), an epoxy layer 56, anda backing layer 58. On either side of the ceramic crystal, there is anelectrode: a positive electrode 61 and a negative electrode 63. Theepoxy layer 56 attaches backing layer 58 to the crystal 54. The entireassembly is contained in a housing 60 which may be made out of, forexample, aluminum. An electrical adapter 62 provides connection forwires to pass through the housing and connect to leads (not shown) whichattach to the crystal 54. Typically, backing layers are designed to adddamping and to create a broadband transducer with uniform displacementacross a wide range of frequency and are designed to suppress excitationat particular vibrational eigen-modes. Wear plates are usually designedas impedance transformers to better match the characteristic impedanceof the medium into which the transducer radiates.

FIG. 6 is a photo of a wear plate 50 with a bubble 64 where the wearplate has pulled away from the ceramic crystal surface due to theoscillating pressure and heating.

FIG. 7A is a cross-sectional view of an ultrasonic transducer 81 of thepresent disclosure, which can be used with the acoustophoretic separatorof FIG. 3. Transducer 81 has an aluminum housing 82. A PZT crystal 86defines the bottom end of the transducer, and is exposed from theexterior of the housing. The crystal is supported on its perimeter by asmall elastic layer 98, e.g. silicone or similar material, locatedbetween the crystal and the housing. Put another way, no wear layer ispresent.

Screws (not shown) attach an aluminum top plate 82 a of the housing tothe body 82 b of the housing via threads 88. The top plate includes aconnector 84 to pass power to the PZT crystal 86. The bottom and topsurfaces of the PZT crystal 86 are each connected to an electrode(positive and negative), such as silver or nickel. A wrap-aroundelectrode tab 90 connects to the bottom electrode and is isolated fromthe top electrode. Electrical power is provided to the PZT crystal 86through the electrodes on the crystal, with the wrap-around tab 90 beingthe ground connection point. Note that the crystal 86 has no backinglayer or epoxy layer as is present in FIG. 5. Put another way, there isan air gap 87 in the transducer between aluminum top plate 82 a and thecrystal 86 (i.e. the air gap is completely empty). A minimal backing 58and/or wear plate 50 may be provided in some embodiments, as seen inFIG. 7B.

The transducer design can affect performance of the system. A typicaltransducer is a layered structure with the ceramic crystal bonded to abacking layer and a wear plate. Because the transducer is loaded withthe high mechanical impedance presented by the standing wave, thetraditional design guidelines for wear plates, e.g., half wavelengththickness for standing wave applications or quarter wavelength thicknessfor radiation applications, and manufacturing methods may not beappropriate. Rather, in one embodiment of the present disclosure thetransducers, there is no wear plate or backing, allowing the crystal tovibrate in one of its eigenmodes with a high Q-factor. The vibratingceramic crystal/disk is directly exposed to the fluid flowing throughthe flow chamber.

Removing the backing (e.g. making the crystal air backed) also permitsthe ceramic crystal to vibrate at higher order modes of vibration withlittle damping (e.g. higher order modal displacement). In a transducerhaving a crystal with a backing, the crystal vibrates with a moreuniform displacement, like a piston. Removing the backing allows thecrystal to vibrate in a non-uniform displacement mode. The higher orderthe mode shape of the crystal, the more nodal lines the crystal has. Thehigher order modal displacement of the crystal creates more trappinglines, although the correlation of trapping line to node is notnecessarily one to one, and driving the crystal at a higher frequencywill not necessarily produce more trapping lines. See the discussionbelow with respect to FIGS. 20-21D.

In some embodiments, the crystal may have a backing that minimallyaffects the Q-factor of the crystal (e.g. less than 5%). The backing maybe made of a substantially acoustically transparent material such asbalsa wood, foam, or cork which allows the crystal to vibrate in ahigher order mode shape and maintains a high Q-factor while stillproviding some mechanical support for the crystal. The backing layer maybe a solid, or may be a lattice having holes through the layer, suchthat the lattice follows the nodes of the vibrating crystal in aparticular higher order vibration mode, providing support at nodelocations while allowing the rest of the crystal to vibrate freely. Thegoal of the lattice work or acoustically transparent material is toprovide support without lowering the Q-factor of the crystal orinterfering with the excitation of a particular mode shape.

Placing the crystal in direct contact with the fluid also contributes tothe high Q-factor by avoiding the dampening and energy absorptioneffects of the epoxy layer and the wear plate. Other embodiments mayhave wear plates or a wear surface to prevent the PZT, which containslead, contacting the host fluid. The face of the piezoelectric elementmay be covered with a film to provide a barrier to divide the elementfrom the fluid. Such a barrier may be desirable in, for example,biological applications such as separating blood. Such applicationsmight use a wear layer such as chrome, electrolytic nickel, orelectroless nickel. Chemical vapor deposition could also be used toapply a layer of poly(p-xylylene) (e.g. Parylene) or other polymer.Organic and biocompatible coatings such as silicone or polyurethane arealso usable as a wear surface. The wear surface or film may beacoustically transparent.

In the present systems, the system is operated at a voltage such thatthe particles are trapped in the ultrasonic standing wave, i.e., remainin a stationary position. The particles are collected in alongwell-defined trapping lines, separated by half a wavelength. Within eachnodal plane, the particles are trapped in the minima of the acousticradiation potential. The axial component of the acoustic radiation forcedrives the particles, with a positive contrast factor, to the pressurenodal planes, whereas particles with a negative contrast factor aredriven to the pressure anti-nodal planes. The radial or lateralcomponent of the acoustic radiation force is the force that traps theparticle. In systems using typical transducers, the radial or lateralcomponent of the acoustic radiation force is typically several orders ofmagnitude smaller than the axial component of the acoustic radiationforce. On the contrary, the lateral force in the separators shown inFIG. 1A, FIG. 1B, FIG. 3 and FIG. 27 can be significant, on the sameorder of magnitude as the axial force component, and is sufficient toovercome the fluid drag force at linear velocities of up to 1 cm/s. Asdiscussed above, the lateral force can be increased by driving thetransducer in higher order mode shapes, as opposed to a form ofvibration where the crystal effectively moves as a piston having auniform displacement. The acoustic pressure is proportional to thedriving voltage of the transducer. The electrical power is proportionalto the square of the voltage.

In embodiments, the pulsed voltage signal driving the transducer canhave a sinusoidal, square, sawtooth, or triangle waveform; and have afrequency of 500 kHz to 10 MHz. The pulsed voltage signal can be drivenwith pulse width modulation, which produces any desired waveform. Thepulsed voltage signal can also have amplitude or frequency modulationstart/stop capability to eliminate streaming.

FIG. 8 is a computer model of an acoustophoretic separator 92 simulatedto produce FIGS. 9A-9D and FIGS. 11-17. The piezo ceramic crystal 94 isin direct contact with the fluid in the water channel 96. A layer ofsilicon 98 is between the crystal 94 and the aluminum top plate 100. Areflector 102 reflects the waves to create standing waves. The reflectoris made of a high acoustic impedance material such as steel or tungsten,providing good reflection. For reference, the Y-axis 104 will bereferred to as the axial direction. The X-axis 106 will be referred toas the radial or lateral direction. The acoustic pressure and velocitymodels were calculated including piezo-electric models of the PZTtransducer, linear elastic models of the surrounding structure (e.g.reflector plate and walls), and a linear acoustic model of the waves inthe water column. The radiation force acting on a suspended particle wascalculated using Gor′kov's formulation. The particle and fluid materialproperties, such as density, speed of sound, and particle size, areentered into the program, and used to determine the monopole and dipolescattering contributions. The acoustic radiation force is determined byperforming a gradient operation on the field potential U, which is afunction of the volume of the particle and the time averaged potentialand kinetic energy of the acoustic field.

In a typical experiment, the system is operated at a voltage such thatthe particles are trapped in the ultrasonic standing wave, i.e., remainin a stationary position. The axial component of the acoustic radiationforce drives the particles, with a positive contrast factor, to thepressure nodal planes, whereas particles with a negative contrast factorare driven to the pressure anti-nodal planes. The radial or lateralcomponent of the acoustic radiation force contributes to trapping theparticle and can be larger than the combined effect of fluid drag forceand gravitational force. For small particles or emulsions the drag forceFD can be expressed as:

${{\overset{\rightarrow}{F}}_{D} = {4\; \pi \; \mu_{f}{{R_{p}\left( {{\overset{\rightarrow}{U}}_{f} - {\overset{\rightarrow}{U}}_{p}} \right)}\left\lbrack \frac{1 + {\frac{3}{2}\hat{\mu}}}{1 + \hat{\mu}} \right\rbrack}}},$

where U_(f) and U_(p) are the fluid and particle velocity, R_(p) is theparticle radius, μ_(f) and μ_(p) are the dynamic viscosity of the fluidand particle, and {circumflex over (μ)}=μ_(p)/μ_(f) is the ratio ofdynamic viscosities. The buoyancy force F_(B) is expressed as:

$F_{B} = {\frac{4}{3}\pi \; {{r_{P}^{3}\left( {\rho_{f} - \rho_{p}} \right)}.}}$

To obtain an expression for lateral acoustic radiation force F_(LRF)when a particle is trapped in the ultrasonic standing wave, the forcebalance on the particle is set to zero. The expression is given by:

F _(LRF) =F _(D) +F _(B)

For a particle of known size and material property, and for a given flowrate, this equation can be used to estimate the magnitude of the lateralacoustic radiation force.

The theoretical model that is used to calculate the acoustic radiationforce is the formulation developed by Gor′kov. The primary acousticradiation force F_(A) is defined as a function of a field potential U,F_(A)=−∇(U),

where the field potential U is defined as

${U = {V_{0}\left\lbrack {{\frac{\langle p^{2}\rangle}{2\; \rho_{f}c_{f}^{2}}f_{1}} - {\frac{3\; \rho_{f}{\langle u^{2}\rangle}}{4}f_{2}}} \right\rbrack}},$

and f₁ and f₂ are the monopole and dipole contributions defined by

${f_{1} = {1 - \frac{1}{\Lambda \; \sigma^{2}}}},{f_{2} = \frac{2\left( {\Lambda - 1} \right)}{{2\; \Lambda} + 1}},$

where p is the acoustic pressure, u is the fluid particle velocity,

is the ratio of particle density ρ_(p) to fluid density ρ_(f), σ is theratio of particle sound speed c_(p) to fluid sound speed C_(f), andV_(o) is the volume of the particle. For a one dimensional standingwave, where the acoustic pressure is expressed as

p=A cos(kx)cos(ωt),

where A is the acoustic pressure amplitude, k is the wavenumber, and wis the angular frequency. In this case, there is only the axialcomponent of the acoustic radiation force F_(ARF), which is found to be

${F_{ARF} = {V_{0}{kX}\frac{A^{2}}{4\; \rho_{f}c_{f}^{2}}{\sin \left( {2\; {kx}} \right)}}},$

where X is the contrast factor given by

$X = {\left( {\frac{{5\; \Lambda} - 2}{1 + {2\; \Lambda}} - \frac{1}{\sigma^{2}\Lambda}} \right).}$

Particles with a positive contrast factor will be driven to the pressurenodal planes, and particles with a negative contrast factor will bedriven to the pressure anti-nodal planes.

Gor′kov's theory is limited to particle sizes that are small withrespect to the wavelength of the sound fields in the fluid and theparticle, and it also does not take into account the effect of viscosityof the fluid and the particle on the radiation force. Additionalnumerical models have been developed for the calculation of the acousticradiation force for a particle without any restriction as to particlesize relative to wavelength. These models also include the effect offluid and particle viscosity, and therefore are a more accuratecalculation of the acoustic radiation force. The models that wereimplemented are based on the theoretical work of Yurii Ilinskii andEvgenia Zabolotskaya.

FIGS. 9A-9D show simulations of the difference in trapping pressuregradients between a single acoustic wave and a multimode acoustic wave.FIG. 9A shows the axial force associated with a single standing acousticwave. FIG. 9B shows the lateral force due to a single standing acousticwave. FIGS. 9C and 9D show the axial force and lateral force,respectively, in a multi-mode (higher order vibration modes havingmultiple nodes) piezoelectric crystal excitation where multiple standingwaves are formed. The electrical input is the same as the single mode ofFIGS. 9A and 9B, but the trapping force (lateral force) is 70 timesgreater (note the scale to the right in FIG. 9B compared to 9D). Thefigures were generated by a computer modeling simulation of a 1 MHzpiezo-electric transducer driven by 10 V AC potted in an aluminum topplate in an open water channel terminated by a steel reflector (see FIG.8). The field in FIGS. 9A and 9B is 960 kHz with a peak pressure of 400kPa. The field in FIGS. 9C and 9D is 961 kHz with a peak pressure of1400 kPa. In addition to higher forces, the 961 kHz field (FIGS. 9C andD) has more gradients and focal spots.

FIG. 10 shows a three dimensional computer generated model of a modeshape calculation showing the out-of-plane displacement for a circularcrystal driven at a frequency of 1 MHz.

FIGS. 11-17 are based on the model of FIG. 8 with a PZT-8 piezo-electrictransducer operating at 2 MHz. The transducer is 1″ wide and 0.04″thick, potted in an aluminum top plate (0.125″ thick) in a 4″×2″ waterchannel terminated by a steel reflector plate (0.180″ thick). Theacoustic beam spans a distance of 2″. The depth dimension, which is 1″,is not included in the 2D model. The transducer is driven at 15V and afrequency sweep calculation is done to identify the various acousticresonances. The results of the three consecutive acoustic resonancefrequencies, i.e., 1.9964 MHz (FIGS. 11, 12, and 13), 2.0106 MHz (FIGS.14 and 15), and 2.025 MHz (FIGS. 16 and 17), are shown. The acousticradiation force is calculated for an oil droplet with a radius of 5micron, a density of 880 kg/m³, and speed of sound of 1700 m/sec. Wateris the main fluid with a density of 1000 kg/m³, speed of sound of 1500m/sec, and dynamic viscosity of 0.001 kg/msec. FIG. 11 shows the lateral(horizontal) acoustic radiation force. FIG. 12 shows the axial(vertical) component for a resonance frequency of 1.9964 MHz. FIG. 13shows the acoustic pressure amplitude.

FIGS. 11-15 show relatively low lateral trapping forces. FIGS. 16-17show that the relative magnitude of the lateral and axial component ofthe radiation force are very similar, indicating that it is possible tocreate large trapping forces, where the lateral force component is ofsimilar magnitude or higher than the axial component. This phenomenon isa new result and contradicts typical results mentioned in theliterature.

A second result is that the acoustic trapping force magnitude exceedsthat of the fluid drag force, for typical flow velocities on the orderof mm/s, and it is therefore possible to use this acoustic field to trapthe oil droplet. Of course, trapping at higher flow velocities can beobtained by increasing the applied power to the transducer. That is, theacoustic pressure is proportional to the driving voltage of thetransducer. The electrical power is proportional to the square of thevoltage.

A third result is that at the frequency shown, high trapping forcesassociated with this particular trapping mode extend across the entireflow channel, thereby enabling capture of oil droplets across the entirechannel width. Finally, a comparison of the minima of the acoustictrapping force field, i.e., the locations of the trapped particles, withthe observed trapping locations of droplets in the standing wave showsgood agreement, indicating that modeling is indeed an accurate tool forthe prediction of the acoustic trapping of particles.

FIG. 14 shows the lateral acoustic radiation force component at aresonance frequency of 2.0106 MHz, and FIG. 15 shows the axial acousticradiation force component at a resonance frequency of 2.0106 MHz. FIGS.14 and 15 exhibit higher peak trapping forces than FIGS. 11 and 12. Thelateral acoustic radiation forces exceed the axial radiation force.However, the higher trapping forces are located in the upper part of theflow channel, and do not span the entire depth of the flow channel. Itwould therefore represent a mode that is effective at trapping particlesin the upper portion of the channel, but not necessarily across theentire channel. Again, a comparison with measured trapping patternsindicates the existence of such modes and trapping patterns.

FIG. 16 shows the lateral force component at a resonance frequency of2.025 MHz, and FIG. 17 shows the axial acoustic radiation forcecomponent at a resonance frequency of 2.025 MHz. The acoustic field canbe significantly different at each acoustic resonance frequency, so adesirable frequency can be located and tracked for operation of thesystem. Two-dimensional (2D) models may be used for accurate predictionof the acoustic trapping forces.

2D axisymmetric models were developed to calculate the trapping forcesfor circular transducers. The models were used to predict acoustictrapping forces on particles, which can then be used to predict particletrajectories in combination with the action of fluid drag and buoyancyforces. The models clearly show that it is possible to generate lateralacoustic trapping forces to trap particles and overcome the effects ofbuoyancy and fluid drag. The models also show that circular transducersdo not provide for large trapping forces across the entire volume of thestanding wave created by the transducer, indicating that circulartransducers yield high trapping forces near the center of the ultrasonicstanding wave generated by the transducer, and provide smaller trappingforces toward the edges of the standing wave. This configuration furtherindicates that the circular transducer provides trapping for a sectionof the fluid flow that would flow across the standing wave of thecircular transducer, and little or no trapping near the edges of thestanding wave.

FIG. 18 is a lin-log graph (linear y-axis, logarithmic x-axis) thatshows the scaling of the acoustic radiation force, fluid drag force, andbuoyancy force with particle radius. Calculations are done for a typicalSAE-30 oil droplet used in experiments. The buoyancy force is a particlevolume dependent force, and is therefore negligible for particle sizeson the order of micron, but grows, and becomes significant for particlesizes on the order of hundreds of microns. The fluid drag force scaleslinearly with fluid velocity, and therefore typically exceeds thebuoyancy force for micron sized particles, but is negligible for largersized particles on the order of hundreds of microns. The acousticradiation force scaling is different. When the particle size is small,Gor′kov's equation is accurate and the acoustic trapping force scaleswith the volume of the particle. Eventually, when the particle sizegrows, the acoustic radiation force no longer increases with the cube ofthe particle radius, and will rapidly vanish at a certain criticalparticle size. For further increases of particle size, the radiationforce increases again in magnitude but with opposite phase (not shown inthe graph). This pattern repeats for increasing particle sizes.

Initially, when a suspension is flowing through the system withprimarily small micron sized particles, the acoustic radiation force canbe employed to balance the combined effect of fluid drag force andbuoyancy force for a particle to be trapped in the standing wave. InFIG. 18 this happens for a particle size of about 3.5 micron, labeled asRd. The graph then indicates that all larger particles will be trappedas well. Therefore, when small particles are trapped in the standingwave, particles coalescence/clumping/aggregation/agglomeration takesplace, resulting in continuous growth of effective particle size. As theparticle size grows, the acoustic radiation force reflects off theparticle, such that large particles will cause the acoustic radiationforce to decrease. Particle size growth continues until the buoyancyforce becomes dominant, which is indicated by a second critical particlesize, R_(c2), at which size the particles will rise or sink, dependingon their relative density with respect to the host fluid. As theparticles rise or sink, they no longer reflect the acoustic radiationforce, so that the acoustic radiation force then increases. Not allparticles will drop out, and those remaining particles will continue togrow in size as well. This phenomenon explains the quick drops and risesin the acoustic radiation force beyond size R_(c2). Thus, FIG. 18explains how small particles can be trapped continuously in a standingwave, grow into larger particles or clumps, and then eventually willrise or settle out because of increased buoyancy force.

Because the circular transducers do not provide for large trappingforces across the entire volume, the effect of transducer shape on oilseparation efficiency was investigated. A 1″-diameter circular PZT-8crystal (FIG. 19, 110) and a 1″×1″ square crystal (FIG. 19, 112) wereused. Otherwise the experiment was run at identical conditions. Table 1shows the results.

TABLE 1 Results of Investigation of Round and Square Transducer ShapeTotal Power Capture Transducer Input Flow rate Duration Efficiency Shape(Watts) (ml/min) (min) (%) Round 20 500 30 59% Square 20 500 30 91%

The results indicate that the square transducer 112 provides better oilseparation efficiencies than the round transducer 110, explained by thefact that the square transducer 112 provides better coverage of the flowchannel with acoustic trapping forces, and that the round transduceronly provides strong trapping forces along the centerline of thestanding wave, confirming the findings of the numerical simulations.

The size, shape, and thickness of the transducer determine thetransducer displacement at different frequencies of excitation, which inturn affects oil separation efficiency. Typically, the transducer isoperated at frequencies near the thickness resonance frequency (halfwavelength). Gradients in transducer displacement typically result inmore places for oil to be trapped. Higher order modal displacementsgenerate three-dimensional acoustic standing waves with strong gradientsin the acoustic field in all directions, thereby creating equally strongacoustic radiation forces in all directions, leading to multipletrapping lines, where the number of trapping lines correlate with theparticular mode shape of the transducer.

FIG. 20 shows the measured electrical impedance amplitude of thetransducer as a function of frequency in the vicinity of the 2.2 MHztransducer resonance. The minima in the transducer electrical impedancecorrespond to acoustic resonances of the water column and representpotential frequencies for operation. Numerical modeling has indicatedthat the transducer displacement profile varies significantly at theseacoustic resonance frequencies, and thereby directly affects theacoustic standing wave and resulting trapping force. Since thetransducer operates near its thickness resonance, the displacements ofthe electrode surfaces are essentially out of phase. The typicaldisplacement of the transducer electrodes is not uniform and variesdepending on frequency of excitation. As an example, at one frequency ofexcitation with a single line of trapped oil droplets, the displacementhas a single maximum in the middle of the electrode and minima near thetransducer edges. At another excitation frequency, the transducerprofile has multiple maxima leading to multiple trapped lines of oildroplets. Higher order transducer displacement patterns result in highertrapping forces and multiple stable trapping lines for the captured oildroplets.

To investigate the effect of the transducer displacement profile onacoustic trapping force and oil separation efficiencies, an experimentwas repeated ten times, with all conditions identical except for theexcitation frequency. Ten consecutive acoustic resonance frequencies,indicated by circled numbers 1-9 and letter A on FIG. 20, were used asexcitation frequencies. The conditions were experiment duration of 30min, a 1000 ppm oil concentration of approximately 5-micron SAE-30 oildroplets, a flow rate of 500 ml/min, and an applied power of 20 W.

As the emulsion passed by the transducer, the trapping lines of oildroplets were observed and characterized. The characterization involvedthe observation and pattern of the number of trapping lines across thefluid channel, as shown in FIG. 21A, for seven of the ten resonancefrequencies identified in FIG. 20.

FIG. 21B shows an isometric view of the system in which the trappingline locations are being determined. FIG. 21C is a view of the system asit appears when looking down the inlet, along arrow 114. FIG. 21D is aview of the system as it appears when looking directly at the transducerface, along arrow 116.

The effect of excitation frequency clearly determines the number oftrapping lines, which vary from a single trapping line at the excitationfrequency of acoustic resonance 5 and 9, to nine trapping lines foracoustic resonance frequency 4. At other excitation frequencies four orfive trapping lines are observed. These experimentally observed resultsconfirm the results expected from the differences when FIGS. 9A and 9Bare compared to FIGS. 9C and 9D. Different displacement profiles of thetransducer can produce different (more) trapping lines in the standingwaves, with more gradients in displacement profile generally creatinghigher trapping forces and more trapping lines.

Table 2 summarizes the findings from an oil trapping experiment using asystem similar to FIG. 27A. An important conclusion is that the oilseparation efficiency of the acoustic separator is directly related tothe mode shape of the transducer. Higher order displacement profilesgenerate larger acoustic trapping forces and more trapping linesresulting in better efficiencies. A second conclusion, useful forscaling studies, is that the tests indicate that capturing 5 micron oildroplets at 500 ml/min uses 10 Watts of power per square-inch oftransducer area per 1″ of acoustic beam span. The main dissipation isthat of thermo-viscous absorption in the bulk volume of the acousticstanding wave. The cost of energy associated with this flow rate is0.667 kWh per cubic meter.

TABLE 2 Trapping Pattern Capture Efficiency Study Resonance Total Power# of Capture Peak Input Trapping Flow rate Duration Efficiency Location(Watts) Lines (ml/min) (min) (%) 4 20 9 500 30 91% 8 20 5 500 30 58% A20 4 500 30 58% 9 20 2 500 30 37%

FIGS. 22 and 23 show photos of the trapped oil droplets in the ninetrapping line pattern. Dashed lines are superimposed over the trappinglines. FIG. 24 shows the pressure field that matches the 9 trapping linepattern. The numerical model is a two-dimensional model; and thereforeonly three trapping lines are observed. Two more sets of three trappinglines exist in the third dimension perpendicular to the plane of the 2Dmodel of FIG. 22 and FIG. 23. This comparison indicates that thenumerical model is accurate in predicting the nature of the ultrasonicstanding wave and the resulting trapping forces, again confirming theresults expected from the differences when FIGS. 9A and 9B are comparedto FIGS. 9C and 9D.

In larger systems, different transducer arrangements are feasible. FIG.25 shows a transducer array 120 including three square 1″×1″ crystals120 a, 120 b, 120 c. Two squares are parallel to each other, and thethird square is offset to form a triangular pattern and get 100%acoustic coverage. FIG. 26 shows a transducer array 122 including tworectangular 1″×2.5″ crystals 122 a, 122 b arranged with their long axesparallel to each other. Power dissipation per transducer was 10 W per1″×1″ transducer cross-sectional area and per inch of acoustic standingwave span in order to get sufficient acoustic trapping forces. For a 4″span of an intermediate scale system, each 1″×1″ square transducerconsumes 40 W. The larger 1″×2.5″ rectangular transducer uses 100 W inan intermediate scale system. The array of three 1″×1″ squaretransducers would consume a total of 120 W and the array of two 1″×2.5″transducers would consume about 200 W. Arrays of closely spacedtransducers represent alternate potential embodiments of the technology.Transducer size, shape, number, and location can be varied as desired togenerate desired three-dimensional acoustic standing waves.

A 4″ by 2.5″ flow cross sectional area intermediate scale apparatus 124for separating a host fluid from a buoyant fluid or particulate is shownin FIG. 27A. The acoustic path length is 4″. The apparatus is shown herein an orientation where the flow direction is downwards, which is usedfor separating less-dense particles from the host fluid. However, theapparatus may be essentially turned upside down to allow separation ofparticles which are heavier than the host fluid. Instead of a buoyantforce in an upward direction, the weight of the agglomerated particlesdue to gravity pulls them downward. It should be noted that thisembodiment is depicted as having an orientation in which fluid flowsvertically. However, it is also contemplated that fluid flow may be in ahorizontal direction, or at an angle.

A particle-containing fluid enters the apparatus through inlets 126 intoan annular plenum 131. The annular plenum has an annular inner diameterand an annular outer diameter. Two inlets are visible in thisillustration, though it is contemplated that any number of inlets may beprovided as desired. In particular embodiments, four inlets are used.The inlets are radially opposed and oriented.

A contoured nozzle wall 129 reduces the outer diameter of the flow pathin a manner that generates higher velocities near the wall region andreduces turbulence, producing near plug flow as the fluid velocityprofile develops, i.e. the fluid is accelerated downward in thedirection of the centerline with little to no circumferential motioncomponent and low flow turbulence. This generates a chamber flow profilethat is optimum for acoustic separation and particle collection. Thefluid passes through connecting duct 127 and into a flow/separationchamber 128. As seen in the zoomed-in contoured nozzle 129 in FIG. 27B,the nozzle wall also adds a radial motion component to the suspendedparticles, moving the particles closer to the centerline of theapparatus and generating more collisions with rising, buoyantagglomerated particles. This radial motion will allow for optimumscrubbing of the particles from the fluid in the connecting duct 127prior to reaching the separation chamber. The contoured nozzle wall 129directs the fluid in a manner that generates large scale vortices at theentrance of the collection duct 133 to also enhance particle collection.Generally, the flow area of the device 124 is designed to be continuallydecreasing from the annular plenum 131 to the separation chamber 128 toassure low turbulence and eddy formation for better particle separation,agglomeration, and collection. The nozzle wall has a wide end and anarrow end. The term scrubbing is used to describe the process ofparticle/droplet agglomeration, aggregation, clumping or coalescing,that occurs when a larger particle/droplet travels in a directionopposite to the fluid flow and collides with smaller particles, ineffect scrubbing the smaller particles out of the suspension.

Returning to FIG. 27A, the flow/separation chamber 128 includes atransducer array 130 and reflector 132 on opposite sides of the chamber.In use, standing waves 134 are created between the transducer array 130and reflector 132. These standing waves can be used to agglomerateparticles, and this orientation is used to agglomerate particles thatare buoyant (e.g. oil). Fluid, containing residual particles, then exitsthrough flow outlet 135.

As the buoyant particles agglomerate, they eventually overcome thecombined effect of the fluid flow drag forces and acoustic radiationforce, and their buoyant force 136 is sufficient to cause the buoyantparticles to rise upwards. In this regard, a collection duct 133 issurrounded by the annular plenum 131. The larger particles will passthrough this duct and into a collection chamber 140. This collectionchamber can also be part of an outlet duct. The collection duct and theflow outlet are on opposite ends of the apparatus.

It should be noted that the buoyant particles formed in the separationchamber 128 subsequently pass through the connecting duct 127 and thenozzle wall 129. This causes the incoming flow from the annular plenumto flow over the rising agglomerated particles due to the inward radialmotion imparted by the nozzle wall. This allows the rising particles toalso trap smaller particles in the incoming flow, increasing scrubbingeffectiveness. The length of the connecting duct 127 and the contourednozzle wall 129 thus increase scrubbing effectiveness. Especially higheffectiveness is found for particles with a size of 0.1 microns to 20microns, where efficiency is very low for conventional methods.

The design here provides an optimized velocity profile with low flowturbulence at the inlet to the flow chamber 128, a scrubbing lengthbefore the flow chamber to enhance particle agglomeration and/orcoalescence before acoustic separation, and the use of the collectionvortices to aid particle removal at the collection duct 133.

In experiments carried out with the apparatus of FIG. 27A, transducerarray 120 was installed in system 124, removed, and then transducerarray 122 installed. The arrays were operated in parallel such that eachtransducer was driven by the same voltage signal from the amplifier. Theelectronic drive circuit consisted of a function generator and a 300 WA300 ENI RF amplifier. The results of the testing are shown in Table 3.The first test used only the two of the 1″×1″ square transducers orarray 120, oriented parallel to each other, and was run at a flow rateof 1300 ml/min. It resulted in an oil separation efficiency of 88%. Thenext test involved all three square transducers and a flow rate of 2000ml/min, and yielded an efficiency of 93%. These results are excellentand demonstrate that the technology is scalable to larger flow channelsdriven by arrays of transducers. The next set of tests involved the1″×2.5″ rectangular transducer array 122. For the first test, only onetransducer was run and yielded an efficiency of 87%. The second testwith both transducers operating yielded an efficiency of 97%. For the1″×2.5″ transducers, the power level that was used was based onoperating the transducer at safe levels. For these tests, the cost ofenergy for the intermediate system is 1 kWh per cubic meter.

TABLE 3 Intermediate System Test Results Total Number of Power FlowCapture Transducer Transducers Input rate Duration EfficiencyConfiguration Active (Watts) (ml/min) (min) (%) 1″ × 1″   2 80 1300 1588% Transducers 1″ × 1″   3 120 2000 15 93% Transducers 1″ × 2.5″ 1 1002000 8 87% Transducers 1″ × 2.5″ 2 100 1000 15 97% Transducers

Numerical modeling was also done for the intermediate sized system witha span of 4″ for the acoustic standing wave. Multiple transducers weremodeled to investigate the coupling effect between transducers.Frequency sweeps were performed and the resonance frequencies for whichthe acoustic mode shapes couple strongly to the higher order mode shapesof the transducer were identified. The comparisons between numerical andexperimental results are excellent and demonstrate the accuracy of themodels. FIG. 28 shows the acoustic pressure field of a model with twotransducers on the right side. A photograph of the trapped oil dropletsin the standing wave is shown in FIG. 29. Both experiment and model showidentical features. At certain excitation frequencies, oil droplets weretrapped in the standing wave well outside the fluid volume defined bythe transducer area, indicating an expanded acoustic field with strongtrapping forces. FIG. 30 shows a photograph of such trapped oildroplets. FIG. 31 shows an acoustic pressure field model which predictsidentical features.

The transducer is typically a thin piezoelectric plate, which isoperated in the (3,3) mode, with electric field in the z-axis andprimary displacement in the z-axis, as shown in FIG. 38A. The transduceris typically coupled on one side by air (i.e. the air gap within thetransducer) and on the other side by water (i.e. the host fluid). Thetypes of waves generated in the plate are known as composite waves. Asubset of composite waves in the piezoelectric plate is similar to leakysymmetric (also referred to as compressional or extensional) Lamb waves.The piezoelectric nature of the plate typically results in theexcitation of symmetric Lamb waves. The waves are leaky because theyradiate into the water layer, which result in the generation of theacoustic standing waves in the water layer. Symmetric Lamb waves havedisplacement profiles that are symmetric with respect to the neutralaxis of the plate, as is shown on the left-hand side of FIG. 32.Symmetric Lab waves seem to be more desirable that anti-symmetric Lambwaves, as is shown on the right hand side of FIG. 32. Lamb waves existin thin plates of infinite extent with stress free conditions on itssurfaces. Because the transducers of this embodiment are finite innature the actual modal displacements are more complicated. FIG. 33shows the typical variation of the in-plane displacement(x-displacement) and out-of-plane displacement (y-displacement) acrossthe thickness of the plate, the in-plane displacement being an evenfunction across the thickness of the plate and the out-of-planedisplacement being an odd function. Because of the finite size of theplate, the displacement components vary across the width and length ofthe plate. An example is shown in FIG. 38A, which illustrates the (3,3)displacement mode. The out-of-plane component is characterized by threeperiodic undulations and the in-plane component by three oscillations.This displacement profile of the transducer is referred to as a (3,3)mode. Additional higher frequency oscillations are seen in thedisplacement profile, e.g., an oscillation with 25 peaks, which is the25th harmonic of the fundamental longitudinal mode in the width andlength direction, since the width and length to thickness ratio is 25for the given transducer. In general, a (m,n) mode is a displacementmode of the transducer in which there are m undulations in transducerdisplacement in the width direction and n undulations in the lengthdirection, and with the thickness variation as described in FIG. 33. Themaximum number of m and n is a function of the dimension of the crystaland the frequency of excitation.

As previously discussed, the transducers are driven so that thepiezoelectric crystal vibrates in higher order modes of the generalformula (m, n), where m and n are independently 1 or greater. FIGS. 34A,34B, 34C and 34D; 35A, 35B and 35C; 36A, 36B and 36C; 37A, 37B and 37C;and 38A, 38B; 38C and 38D show, as grouped, in order, illustrations ofvibration modes (1,1), (2,1), (1,2), (2,2), and (3,3) of a rectangularplate. In each figure, the plate 156 has a length 150 that is equal toor longer than its width 152. A perspective view, a view along thelength (y=0), and a view along the width (x=0) are provided for eachvibration mode.

FIGS. 34A, 34B, 34C and 34D show the vibration mode (1,1). In this mode,the plate has its maximal displacement at antinode 154 in the center ofthe rectangular plate 156. FIG. 34B shows the view along the length 150(i.e. along arrow 151) and FIG. 34C shows the view along the width 152(along arrow 153). FIG. 34D shows the in-plane displacement associatedwith vibration mode (1,1).

FIGS. 35A, 35B and 35C show mode (2,1). Here, there are two antinodes160 (peaking above the plane of the membrane 156). These two antinodesare on opposite sides of a nodal line of minimal displacement 162 whichruns parallel to width 152 and at the center of length 150. Note that inthe case of a square transducer (one in which length 150 is equal towidth 152, as in the transducer 112 of FIG. 19 and in FIG. 25), the(1,2) and (2,1) modes are mere rotations of each other. FIG. 35B showsthe view along the length (i.e. along arrow 161) and FIG. 35C shows theview along the width (i.e. along arrow 163).

FIG. 36A shows mode (1,2). This mode also has two antinodes 166 and onenodal line 164. Compared to FIG. 35A, the difference here is that thenodal line 164 runs lengthwise (parallel to length 150) and at thecenter of width 152. FIG. 36B shows the view along arrow 165 and FIG.36C shows the view along arrow 167.

FIG. 37A, shows the (2,2) mode, which has four antinodes 174 and twonodal lines 170, 176. One nodal line 176 is in the center of width 152,parallel to length 150. The other nodal line 170 is in the center oflength 150, parallel to width 152. FIG. 37B shows the view along arrow171 and FIG. 37C shows the view along arrow 173.

FIG. 38A shows the vibration mode (3,3). There are two lengthwise nodallines 186 and two width-wise nodal lines 180. Three sets of antinodes182 are created by the nodal lines 180, and three sets of antinodes 184are created by the nodal lines 186. This results in a total of nineantinodes resulting from their intersection in each direction. FIG. 38Bshows the view along arrow 181 and FIG. 38C shows the view along arrow183. FIG. 38D shows the in-plane displacement associated with vibrationmode (3,3).

These modes are illustrative and, generally, the transducers willvibrate in higher order modes than (2,2). Higher order modes willproduce more nodes and antinodes, result in three-dimensional standingwaves in the water layer, characterized by strong gradients in theacoustic field in all directions, not only in the direction of thestanding waves, but also in the lateral directions. As a consequence,the acoustic gradients result in stronger trapping forces in the lateraldirection.

FIGS. 39A-39C show the pressure field generated by a transduceroperating at different displacement modes. In each figure, the vibratingcrystal is illustrated at y=1 inch, and the resultant standing wave thatis transmitted into the fluid is illustrated below. FIG. 39A shows themagnitude of the acoustic pressure when the water layer is driven by atransducer operating predominantly at the (1,1) mode. The resultingpressure field is one that can be described as a primarilyone-dimensional standing wave with a slowly varying acoustic pressureamplitude in the lateral direction. FIG. 39B shows the pressure fieldexcited by a transducer operating predominantly at the (2,2) mode, andsimilarly FIG. 39C shows the pressure field when the transducer isoperated predominantly at the (3,3) mode. We observe that a (2,2)excitation leads to the generation of four (2×2) parallel acousticstanding waves, and a (3,3) leads to nine (3×3) standing waves. Theratio of the lateral acoustic radiation force component to the axialcomponent was calculated for these three pressure fields. Excitation atthe (2,2) mode leads to the doubling of that ratio in comparison to the(1,1) mode. Excitation at the (3,3) mode leads to the tripling of theratio of the (1,1) mode, hereby demonstrating the benefit of excitinghigher order modes.

Generally speaking but with specific reference to the transducer arrayof FIG. 27A, the transducer setup of the present disclosure creates athree dimensional pressure field which includes standing wavesperpendicular to the fluid flow. The pressure gradients are large enoughto generate acoustophoretic forces orthogonal to the standing wavedirection (i.e., the acoustophoretic forces are parallel to the fluidflow direction) which are of the same order of magnitude as theacoustophoretic forces in the wave direction. This permits enhancedparticle trapping and collection in the flow chamber and alongwell-defined trapping lines, as opposed to merely trapping particles incollection planes as in conventional devices. The particles havesignificant time to move to nodes or anti-nodes of the standing waves,generating regions where the particles can concentrate, agglomerate,and/or coalesce.

In some embodiments, the fluid flow has a Reynolds number of up to 1500,i.e. laminar flow is occurring. For practical application in industry,the Reynolds number is usually from 10 to 1500 for the flow through thesystem. The particle movement relative to the fluid motion generates aReynolds number much less than 1.0. The Reynolds number represents theratio of inertial flow effects to viscous effects in a given flow field.For Reynolds numbers below 1.0, viscous forces are dominant in the flowfield. This results in significant damping where shear forces arepredominant throughout the flow. This flow where viscous forces aredominant is called Stokes flow, The flow of molasses is an example. Wallcontouring and streamlining have very little importance.

It is associated with the flow of very viscous fluids or the flow invery tiny passages, like MEMS devices. Inlet contouring has littleimportance. The flow of the particles relative to the fluid in FSAparticle separator will be Stokes flow because both the particlediameters and the relative velocities between the particles and fluidare very small. On the other hand, the Reynolds number for the flowthrough the system will be much greater than 1.0 because the fluidvelocity and inlet diameter are much larger. For Reynolds numbers muchgreater than 1.0, viscous forces are dominant only where the flow is incontact with the surface. This viscous region near the surface is calleda boundary layer and was first recognized by Ludwig Prandtl (Reference2). In duct flow, the flow will be laminar if the Reynolds number issignificantly above 1.0 and below 2300 for fully developed flow in theduct. The wall shear stress at the wall will diffuse into the streamwith distance. At the inlet of the duct, flow velocity starts offuniform. As the flow moves down the duct, the effect of wall viscousforces will diffuse inward towards the centerline to generate aparabolic velocity profile. This parabolic profile will have a peakvalue that is twice the average velocity. The length for the parabolicprofile to develop is a function of the Reynolds number. For a Reynoldsnumber of 20, which is typical for CHO operation, the development lengthwill be 1.2 duct diameters. Thus, fully developed flow happens veryquickly. This peak velocity in the center can be detrimental to acousticparticle separation. Also, at laminar flow Reynolds numbers turbulence,can occur and flow surface contouring is very important in controllingthe flow. For these reasons, the separator was designed with an annularinlet plenum and collector tube

The large annular plenum is followed by an inlet wall nozzle thataccelerates and directs the fluid inward toward the centerline as shownin FIG. 27B. The wall contour will have a large effect on the profile.The area convergence increases the flow average velocity, but it is thewall contour that determines the velocity profile. The nozzle wallcontour will be a flow streamline, and is designed with a small radiusof curvature in the separator.

The transducer(s) is/are used to create a pressure field that generatesforces of the same order of magnitude both orthogonal to the standingwave direction and in the standing wave direction. When the forces areroughly the same order of magnitude, particles of size 0.1 microns to300 microns will be moved more effectively towards regions ofagglomeration (“trapping lines”), as seen in FIG. 21C. Because of theequally large gradients in the orthogonal acoustophoretic forcecomponent, there are “hot spots” or particle collection regions that arenot located in the regular locations in the standing wave directionbetween the transducer 130 and the reflector 132. Hot spots are locatedin the maxima or minima of acoustic radiation potential. Such hot spotsrepresent particle collection locations which allow for better wavetransmission between the transducer and the reflector during collectionand stronger inter-particle forces, leading to faster and betterparticle agglomeration.

One application of the acoustophoretic separator is separation of cellsfrom a medium, such as the separation of red blood cells, described inU.S. application Ser. No. 13/866,584 to Dutra and Lipkens, entitled“ACOUSTOPHORETIC SEPARATION OF LIPID PARTICLES FROM RED BLOOD CELLS,”the entirety of which is hereby fully incorporated by reference.

Another application is the separation of a biological therapeuticprotein from the biologic cells that produce the protein. In thisregard, current methods of separation use filtration or centrifugation,either of which can damage cells, releasing protein debris and enzymesinto the purification process and increasing the load on downstreamportions of the purification system. It is desirable to be able toprocess volumes having higher cell densities, because this permitscollection of larger amounts of the therapeutic protein and better costefficiencies.

FIG. 40A and FIG. 40B are exploded views showing the various parts ofacoustophoretic separators. FIG. 40A has only one separation chamber,while FIG. 40B has two separation chambers.

Referring to FIG. 40A, fluid enters the separator 190 through afour-port inlet 191. A transition piece 192 is provided to create plugflow through the separation chamber 193. A transducer 40 and a reflector194 are located on opposite walls of the separation chamber. Fluid thenexits the separation chamber 193 and the separator through outlet 195.

FIG. 40B has two separation chambers 193. A system coupler 196 is placedbetween the two chambers 193 to join them together.

Acoustophoretic separation has been tested on different lines of Chinesehamster ovary (CHO) cells. In one experiment, a solution with a startingcell density of 8.09×10⁶ cells/mL, a turbidity of 1,232 NTU, and cellviability of roughly 75% was separated using a system as depicted inFIG. 40A. The transducers were 2 MHz crystals, run at approximately 2.23MHz, drawing 24-28 Watts. A flow rate of 25 mL/min was used. The resultof this experiment is shown in FIG. 41A.

In another experiment, a solution with a starting cell density of8.09×10⁶ cells/mL, a turbidity of 1,232 NTU, and cell viability ofroughly 75% was separated. This CHO cell line had a bi-modal particlesize distribution (at size 12 μm and 20 μm). The result is shown in FIG.41B.

FIG. 41A and FIG. 41B were produced by a Beckman Coulter Cell ViabilityAnalyzer. Other tests revealed that frequencies of 1 MHz and 3 MHz werenot as efficient as 2 MHz at separating the cells from the fluid.

In other tests at a flow rate of 10 L/hr, 99% of cells were capturedwith a confirmed cell viability of more than 99%. Other tests at a flowrate of 50 mL/min (i.e. 3 L/hr) obtained a final cell density of 3×10⁶cells/mL with a viability of nearly 100% and little to no temperaturerise. In yet other tests, a 95% reduction in turbidity was obtained at aflow rate of 6 L/hr.

Testing on the scaled unit shown in FIG. 27 was performed using yeast asa simulant for CHO for the biological applications. For these tests, ata flow rate of 15 L/hr, various frequencies were tested as well as powerlevels. Table 1 shows the results of the testing.

TABLE 1 2.5″ × 4″ System results at 15 L/hr Flow rate Frequency (MHz) 30Watts 37 Watts 45 Watts 2.2211 93.9 81.4 84.0 2.2283 85.5 78.7 85.42.2356 89.1 85.8 81.0 2.243 86.7 — 79.6

In biological applications, many parts, e.g. the tubing leading to andfrom the housing, inlets, exit plenum, and entrance plenum, may all bedisposable, with only the transducer and reflector to be cleaned forreuse. Avoiding centrifuges and filters allows better separation of theCHO cells without lowering the viability of the cells. The form factorof the acoustophoretic separator is also smaller than a filteringsystem, allowing the CHO separation to be miniaturized. The transducersmay also be driven to create rapid pressure changes to prevent or clearblockages due to agglomeration of CHO cells. The frequency of thetransducers may also be varied to obtain optimal effectiveness for agiven power.

The present disclosure has been described with reference to exemplaryembodiments. Obviously, modifications and alterations will occur toothers upon reading and understanding the preceding detaileddescription. It is intended that the present disclosure be construed asincluding all such modifications and alterations insofar as they comewithin the scope of the appended claims or the equivalents thereof.

1. An apparatus, comprising: a chamber; at least one ultrasonictransducer coupled to the chamber, the transducer including apiezoelectric material that is configured to be driven by a drive signalto create a multi-dimensional acoustic standing wave in the chamber; anda reflector across the chamber from the at least one ultrasonictransducer.
 2. The apparatus of claim 1, wherein the at least oneultrasonic transducer creates a displacement profile containing aharmonic of a fundamental longitudinal mode, resulting in themulti-dimensional acoustic standing wave in the chamber.
 3. Theapparatus of claim 1, wherein the multi-dimensional acoustic standingwave results in an acoustic radiation force with an axial forcecomponent and a lateral force component that are of the same order ofmagnitude.
 4. The apparatus of claim 1, wherein the at least oneultrasonic transducer comprises a plurality of ultrasonic transducersthat span the width of the chamber.
 5. The apparatus of claim 1, whereinthe piezoelectric material is rectangular in shape.
 6. The apparatus ofclaim 1, wherein the multi-dimensional acoustic standing wave is athree-dimensional acoustic standing wave.
 7. The apparatus of claim 1,wherein the reflector includes a non-planar surface.
 8. The apparatus ofclaim 1, wherein the ultrasonic transducer comprises: a housing; thepiezoelectric material at a bottom end that is exposed from an exteriorof the housing; a top plate at a top end of the housing; and an air gapbetween the top plate and the piezoelectric material.
 9. A method forseparating a second fluid or a particulate from a host fluid,comprising: placing a mixture containing the host fluid and the secondfluid or particulate into an apparatus comprising: a chamber; at leastone ultrasonic transducer coupled to the chamber, the transducerincluding a piezoelectric material; and a reflector across the chamberfrom the at least one ultrasonic transducer; and applying a drive signalto drive the at least one ultrasonic transducer to create amulti-dimensional acoustic standing wave in the chamber; wherein thesecond fluid or particulate is trapped in the three dimensionalultrasonic standing wave and separated from the host fluid.
 10. Themethod of claim 9, wherein the piezoelectric material vibrates in ahigher order mode that creates a displacement profile containing aharmonic of a fundamental longitudinal mode, resulting in themulti-dimensional acoustic standing wave in the chamber.
 11. The methodof claim 10, wherein the harmonic is a function of a width to thicknessratio or a length to thickness ratio of the piezoelectric material. 12.The method of claim 10, wherein the displacement profile of the at leastone ultrasonic transducer is symmetric with respect to an axis of thepiezoelectric material.
 13. The method of claim 10, wherein thedisplacement profile of the at least one ultrasonic transducer variesacross a width and a length of the piezoelectric material.
 14. Themethod of claim 9, wherein the multi-dimensional acoustic standing waveresults in an acoustic radiation force that includes an axial forcecomponent and a lateral force component that are of the same order ofmagnitude.
 15. The method of claim 9, wherein the particulate is Chinesehamster ovary (CHO) cells, NS0 hybridoma cells, baby hamster kidney(BHK) cells, or human cells.
 16. The method of claim 9, wherein greaterthan 90% of the particulate is separated from the host fluid on a volumebasis.
 17. The method of claim 9, wherein a frequency of the drivesignal is 100 kHz to 10 MHz.
 18. The method of claim 9, wherein themixture flows from an apparatus inlet through an annular plenum prior toentering the chamber.
 19. A separation system for separating cells froma host fluid, comprising: a separation stage including at least oneultrasonic transducer configured to produce an acoustic standing wavefor trapping cells to produce a clarified host fluid; and a downstreampurification system coupled to the separation stage for receiving theclarified host fluid, wherein the load on the downstream purificationsystem is reduced.
 20. The separation system of claim 19, wherein theseparation stage further comprises a reflector.